TY - JOUR

T1 - “Flux-balance formulae” for extreme mass-ratio inspirals

AU - Isoyama, Soichiro

AU - Fujita, Ryuichi

AU - Nakano, Hiroyuki

AU - Sago, Norichika

AU - Tanaka, Takahiro

N1 - Funding Information:
We thank Leor Barack, Scott Hughes, Maarten van de Meent, Eric Poisson, and Adam Pound for useful discussion and feedback on the manuscript. S.I. is particularly grateful to Riccardo Sturani for his continuous encouragement. S.I. acknowledges the financial support of a JSPS Postdoctoral Fellowship for ResearchAbroad and the Brazilian Ministry of Education – MEC during his stay at IIP-Natal-Brazil. This work was supported in part by JSPS/Ministry of Education, Culture, Sports, Science and Technology (MEXT) KAKENHI Grant Nos. JP16H02183 (R.F.), JP18H04583 (R.F.), JP17H06358 (H.N., N.S., and T.T.), JP16K05347 (H.N.), and JP16K05356 (N.S.).
Publisher Copyright:
© The Author(s) 2019. Published by Oxford University Press on behalf of the Physical Society of Japan.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The “flux-balance formulae” that determine the averaged evolution of energy, azimuthal angular momentum, and Carter constant in terms of the averaged asymptotic gravitational-wave fluxes for inspirals of small bodies into Kerr black holes were first derived about 15 years ago. However, this derivation is restricted to the case that the background Kerr geodesics are non-resonant (i.e., the radial and angular motions are always incommensurate), and excludes the resonant case that can be important for the radiative dynamics of extreme mass-ratio inspirals. We give here a new derivation of the flux formulae based on Hamiltonian dynamics of a self-forced particle motion, which is a valuable tool for analyzing self-force effects on generic (eccentric, inclined) bound orbits in the Kerr spacetime. This Hamiltonian derivation using action-angle variables is much simpler than the previous one, applies to resonant inspirals without any complication, and can be straightforwardly implemented by using analytical/numerical Teukolsky-based flux codes.

AB - The “flux-balance formulae” that determine the averaged evolution of energy, azimuthal angular momentum, and Carter constant in terms of the averaged asymptotic gravitational-wave fluxes for inspirals of small bodies into Kerr black holes were first derived about 15 years ago. However, this derivation is restricted to the case that the background Kerr geodesics are non-resonant (i.e., the radial and angular motions are always incommensurate), and excludes the resonant case that can be important for the radiative dynamics of extreme mass-ratio inspirals. We give here a new derivation of the flux formulae based on Hamiltonian dynamics of a self-forced particle motion, which is a valuable tool for analyzing self-force effects on generic (eccentric, inclined) bound orbits in the Kerr spacetime. This Hamiltonian derivation using action-angle variables is much simpler than the previous one, applies to resonant inspirals without any complication, and can be straightforwardly implemented by using analytical/numerical Teukolsky-based flux codes.

UR - http://www.scopus.com/inward/record.url?scp=85063209933&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063209933&partnerID=8YFLogxK

U2 - 10.1093/ptep/pty136

DO - 10.1093/ptep/pty136

M3 - Article

AN - SCOPUS:85063209933

SN - 2050-3911

VL - 2019

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

IS - 1

M1 - 013E01

ER -